Applications of Emergent Phenomena - Systematic Design for Emergence in Cellular Nonlinear Networks - page 147

The decoder (Fig. 8.13) operates using a very simple search based on the index
J . For each of the most significant m bitplanes, any wxw bit-block is recon-
structed as B ˆ . The bitplanes are then assembled into a “gray-level” image

and submitted to the Median filter which may be applied up to four times in order
to recover the original image. Color images are similarly processed with bitplanes
for each of the three basis colors (R, G, B).

C

J

8.4.2 Detecting the Useful Genes

In what follows we consider the problem of finding genes (within the 2s5 and 2s9
families) such that the patterns produced have a “pink noise” characteristic which
seems to give the best results in the proposed CA-VQ encoding scheme. The siev-
ing method exposed in Chap. 6 is used, using iteratively tuned sieves and based on

the feedback information regarding the codec performance for some test images.
The measures of emergence are those defined in Chaps. 4 and 5, i.e. determined
experimentally.

Let us remind that a clustering coefficient with a value C close to one indicates
a homogeneous state (low frequencies) while a value of C = 0.5 is a feature asso-
ciated with a “white noise” chaotic pattern. At the other extreme C = 0 indicates
the presence of perfectly regular chess-board pattern (i.e. preponderance of high
frequencies in the spectral distribution). We found experimentally that patterns
with
compression method.
In addition let us consider the transient length (Tr) as defined in Chap. 4 and
the exponent of growth ( U ) as defined in Chap. 5.
While having these three synthetic measurements for complexity one can em-
ploy a single to triple sieve to locate some genes of interest for oupr problem. For

C | 0.83 are well suited for building binary codebooks as needed by our

instance, by choosing C 0.5 0.00035 (a single sieve) for the gene space of all

1,024 semi-totalistic genes, the genes with ID = 661, ID = 325 and ID = 650 will
be returned as the best random number generators.

It is interesting to note that ID = 661 has the highest representation complexity

among all genes (it requires m = 8 transitions, while ID = 650 and ID = 325
require a bit less i.e. m = 7, according to Table 3.3 in Chap. 3). Such random gen-

erators may be conveniently used in the encoder to produce a “random” seed from
a pattern with only three randomly placed dots. They can be also used for genera-
ting the ignored bitplanes .

a list of genes that are useful for the purpose of generating codebooks. Running
this sieve actually produced a list of 68 genes. Here we were interested in fast
emergence (

A double sieve defined as: U 0.5 AND C 0.83 0.02 is likely to produce

U ) primarily, and we will call these genes “fast codebooks”.
That is why we would further investigate among the pool of 68 genes only for
those giving the desired codebooks after running the CA for ten iterations. In
this case we take each of the genes from the above list and use it in the CA-VQ

0.5